Question

In figure $A,B$ and $C$ are three points on a circle with centre $O$ such that $\angle BOC={30}^o$ and $\angle AOB={60}^o$. If $D$ is a point on the circle other than the arc $ABC$, find $\angle ADC$.

• A. ${30}^{\circ }$
• B. ${90}^{\circ }$
• C. ${45}^{\circ }$
• D. ${60}^{\circ }$

Answer 1

The correct option is C ${45}^{\circ }$

According to theorem of circles $\angle AOC=2\angle ADC$ .....(i)

$\angle AOC=\angle AOB+\angle BOC={60}^{\circ }+{30}^{\circ }={90}^{\circ }$

from equation(i)

${90}^{\circ }=2\angle ADC$

$\angle ADC={45}^{\circ }$